Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured on, for example, a photosensitive plate by well-known interference techniques to form a holographic recording, or “hologram”, comprising interference fringes. The “hologram” may be reconstructed by illuminating it with suitable light to form a holographic reconstruction, or replay image, representative of the original object.
It has been found that a holographic reconstruction of acceptable quality can be formed from a “hologram” containing only phase information related to the original object. Such holographic recordings may be referred to as phase-only holograms. Computer-generated holography may numerically simulate the interference process, using Fourier techniques for example, to produce a computer-generated phase-only hologram. A computer-generated phase-only hologram may be used to produce a holographic reconstruction representative of an object.
The term “hologram” therefore relates to the recording which contains information about the object and which can be used to form a reconstruction representative of the object. The hologram may contain information about the object in the frequency, or Fourier, domain.
It has been proposed to use holographic techniques in a two-dimensional image projection system. An advantage of projecting images using phase-only holograms is the ability to control many image attributes via the computation method—e.g. the aspect ratio, resolution, contrast and dynamic range of the projected image. A further advantage of phase-only holograms is that no optical energy is lost by way of amplitude modulation.
A computer-generated phase-only hologram may be “pixellated”. That is, the phase-only hologram may be represented on an array of discrete phase elements. Each discrete element may be referred to as a “pixel”. Each pixel may act as a light modulating element such as a phase modulating element. A computer-generated phase-only hologram may therefore be represented on an array of phase modulating elements such as a liquid crystal spatial light modulator (SLM). The SLM may be reflective meaning that modulated light is output from the SLM in reflection.
Each phase modulating element, or pixel, may vary in state to provide a controllable phase delay to light incident on that phase modulating element. An array of phase modulating elements, such as a Liquid Crystal On Silicon (LCOS) SLM, may therefore represent (or “display”) a computationally-determined phase-delay distribution. If the light incident on the array of phase modulating elements is coherent, the light will be modulated with the holographic information, or hologram. The holographic information may be in the frequency, or Fourier, domain.
Alternatively, the phase-delay distribution may be recorded on a kinoform. The word “kinoform” may be used generically to refer to a phase-only holographic recording, or hologram.
The phase delay may be quantised. That is, each pixel may be set at one of a discrete number of phase levels.
The phase-delay distribution may be applied to an incident light wave (by illuminating the LCOS SLM, for example) and reconstructed. The position of the reconstruction in space may be controlled by using an optical Fourier transform lens, to form the holographic reconstruction, or “image”, in the spatial domain. Alternatively, no Fourier transform lens may be needed if the reconstruction takes place in the far-field.
A computer-generated hologram may be calculated in a number of ways, including using algorithms such as Gerchberg-Saxton. The Gerchberg-Saxton algorithm may be used to derive phase information in the Fourier domain from amplitude information in the spatial domain (such as a 2D image). That is, phase information related to the object may be “retrieved” from intensity, or amplitude, only information in the spatial domain. Accordingly, a phase-only holographic representation of an object in the Fourier domain may be calculated.
The holographic reconstruction may be formed by illuminating the Fourier domain hologram and performing an optical Fourier transform, using a Fourier transform lens, for example, to form an image (holographic reconstruction) at a reply field such as on a screen.
FIG. 1 shows an example of using a reflective SLM, such as a LCOS-SLM, to produce a holographic reconstruction at a replay field location, in accordance with the present disclosure.
A light source (110), for example a laser or laser diode, is disposed to illuminate the SLM (140) via a collimating lens (111). The collimating lens causes a generally planar wavefront of light to become incident on the SLM. The direction of the wavefront is slightly off-normal (e.g. two or three degrees away from being truly orthogonal to the plane of the transparent layer). The arrangement is such that light from the light source is reflected off a mirrored rear surface of the SLM and interacts with a phase-modulating layer to form an exiting wavefront (112). The exiting wavefront (112) is applied to optics including a Fourier transform lens (120), having its focus at a screen (125).
The Fourier transform lens (120) receives a beam of phase-modulated light exiting from the SLM and performs a frequency-space transformation to produce a holographic reconstruction at the screen (125) in the spatial domain.
In this process, the light—in the case of an image projection system, the visible light—from the light source is distributed across the SLM (140), and across the phase modulating layer (i.e. the array of phase modulating elements). Light exiting the phase-modulating layer may be distributed across the replay field. Each pixel of the hologram contributes to the replay image as a whole. That is, there is not a one-to-one correlation between specific points on the replay image and specific phase-modulating elements.
The Gerchberg Saxton algorithm considers the phase retrieval problem when intensity cross-sections of a light beam, IA(x,y) and IB(x,y), in the planes A and B respectively, are known and IA(x,y) and IB(x,y) are related by a single Fourier transform. With the given intensity cross-sections, an approximation to the phase distribution in the planes A and B, ΦA(x,y) and ΦB(x,y) respectively, is found. The Gerchberg-Saxton algorithm finds solutions to this problem by following an iterative process.
The Gerchberg-Saxton algorithm iteratively applies spatial and spectral constraints while repeatedly transferring a data set (amplitude and phase), representative of IA(x,y) and IB(x,y), between the spatial domain and the Fourier (spectral) domain. The spatial and spectral constraints are IA(x,y) and IB(x,y) respectively. The constraints in either the spatial or spectral domain are imposed upon the amplitude of the data set. The corresponding phase information is retrieved through a series of iterations.
A holographic projector may be provided using such technology. Such projectors have found application in head-up displays for vehicles.
The use of head-up displays in automobiles is becoming increasing popular. Head-up displays are broken down in to two main categories, those which use a combiner (a free standing glass screen whose purpose is to reflect a virtual image in to the driver's line of sight) and those which utilise the vehicle's windscreen to achieve the same purpose.
FIG. 2 shows an example head-up display comprising a light source 206, a spatial light modulator 204 arranged to spatially modulate light from the light source with holographic data representative of an image for projection, a Fourier transform optic 205, a diffuser 203, a freeform mirror 201, a windscreen 202 and a viewing position 207. FIG. 2 shows a so-called “indirect view” system in which a real image of the holographic reconstruction is formed at a replay field on the diffuser 203. A holographic reconstruction is therefore projected on the diffuser 203 and may be viewed from viewing position 207 by focusing on the diffuser 203. The projected image is viewed via a first reflection off freeform mirror 201 and a second reflection off windscreen 202. The diffuser acts to increase the numerical aperture of the holographic system, fully illuminating the freeform mirrors thereby allowing the virtual image to be viewed by a driver, for example.
However, a problem with using a windscreen 202 as a so-called “combiner” is that the curvature of the windscreen applies lensing power to the virtual image being displayed. This problem is further complicated by the different windscreen curvatures 202 that exist from left to right & top to bottom. Normally this complex lensing function is corrected through the use of a carefully designed freeform mirror 201. However, these mirrors are extremely complex to design with minimal aberrations and are extremely costly to manufacture with the required precision.
The present disclosure aims to address these problems and provide an improved projector.